PPSSPP is a portable PSP emulator created by developer Henrik Rydgard that runs on Linux, Mac OS X, Android and Windows 8.
According to the folks at XDA Devs, PPSSPP is currently ranked as a relatively new project and is therefore somewhat of a work in progress.
As such, not all PSP games work at this time, although the ones that do reportedly run "flawlessly." In the meantime, Rydgard and his dev team are working to bring full PPSSPP support to all games.
Although still in its initial stages, I do believe this particular emulator holds a lot of potential, especially due to its cross-platform nature. Yes, such an approach may very well be slightly overly ambitious, but will definitely be well worth the wait when all the kinks are worked out.
I for one am looking forward to playing classic PSP titles across multiple devices, especially on my Android smartphone.